Grade 12Integral Calculus

integrate the following integral
∫ (3x + 5) / sqrt(7x + 9) dx

taniska

11 Years agoGrade 12

1 Answer

Jitender Singh

11 Years ago

Ans:
Hello Student,
Please find answer to your question below

$I = \int \frac{3x+5}{\sqrt{7x+9}}dx$
$I = 3\int \frac{x+\frac{5}{3}}{\sqrt{7x+9}}dx$
$I = \frac{3}{7}\int \frac{7x+\frac{35}{3}}{\sqrt{7x+9}}dx$
$I = \frac{3}{7}\int \frac{7x+9-9+\frac{35}{3}}{\sqrt{7x+9}}dx$
$I = \frac{3}{7}\int \frac{7x+9+\frac{8}{3}}{\sqrt{7x+9}}dx$ $I = \frac{3}{7}\int \frac{7x+9}{\sqrt{7x+9}}dx+\int \frac{8}{7}.\frac{1}{\sqrt{7x+9}}dx$
$I = \frac{3}{7}\int \sqrt{7x+9}dx+\int \frac{8}{7}.\frac{1}{\sqrt{7x+9}}dx$
$I = \frac{3}{7}\frac{2(7x+9)^{3/2}}{3.7}+\int \frac{8}{7}.\frac{1}{\sqrt{7x+9}}dx$
$I = \frac{2(7x+9)^{3/2}}{49}+\frac{16\sqrt{7x+9}}{49}+c$